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Nuclear and solar thermal propulsion offer enhanced efficiencies for in-space travel which may open up the outer Solar System to both crewed and automated craft. However, these advanced propulsion systems require cutting-edge materials which are often not easily tested in the laboratory. Ab initio thermodynamics and other computational methods offer a way to test materials at high pressures and temperatures more quickly, and with reduced cost. Here, several case studies are presented which highlight the utility of modern simulation techniques. First, an extensive thermodynamic study was performed at the ab initio level to elucidate the role of hot hydrogen flow on the erosion of four refractory carbides to examine their appropriateness for use as channel coatings. A detailed analysis of reaction products informs estimates of erosion which are validated in comparison with heritage NERVA data. Specific material suggestions are made for both nuclear and solar designs. Secondly, we examined the mechanical behavior and chemical stability of various components of an idealized nuclear cermet core design using techniques spanning from the atomic to microscale. Next, the mechanical and chemical behavior of tungsten (a potential matrix material) and the stability of uranium mononitride (a potential ceramic fuel element), are characterized in the presence of hydrogen and at elevated temperatures with ab initio thermodynamics. Finally, the mechanical response and failure of tungsten under tensile strain is simulated at the micron scale with a combined finite element and dislocation dynamics approach. The resultant stress-strain data agrees well with experiments and leads to a workflow which can incorporate ab initio thermodynamic data into micron-scale simulations and thus provide real-world relevant estimates of erosion and stress-strain behavior. The power of this framework and our plans to use it in the future will be discussed.